Exercise: 4.3
Q1. Find the roots of the following quadratic equations, if they exist, by the method of completing the square:
(i) 2x2 - 7x + 3 = 0
Solution: a = 2, b = -7, c = 3Now checking for nature of roots,
D = b2 - 4ac
D = (-7)2 - 4 x 2 x 3
D = 49 - 24
D = 25
Hence D > 0
∴ There is two different and real roots
2x2 - 7x + 3 = 0
Dividing by a term 2 we get.
Putting A term and B term into a2-2ab+b2
(ii) 2x2 + x - 4 = 0;
Solution:
a = 2, b = 1, c = -4
Now checking for nature of roots,
D = b2 - 4ac
D = (1)2 - 4 x 2 x -4
D = 1 - (-32)
D = 1 + 32
D = 33
Hence D > 0
∴ There are two distinct and real roots
2x2 + x - 4 = 0
(iii) 4x2 + 4√3x + 3 = 0
Solution:
a =4, b = 4√3, c= 3
D = b2 - 4ac = (4√3)2 - 4 x 4 x 3
= 48 - 48 = 0
Here D = 0
Therefore, There are two real and equal roots.
4x2 + 4√3x + 3 = 0
⇒(2x)2 + 2 . 2x. √3 + (√3)2 = 0
⇒(2x + √3)2= 0
⇒ (2x + √3) (2x + √3) = 0
⇒ 2x + √3 = 0, 2x + √3 = 0
⇒ 2x = - √3, 2x = - √3
⇒ x = √3/2, x = √3/2
(iv) 2x2 + x + 4 = 0;
a = 2, b = 1, c = 4Now checking for nature of roots,
D = b2 - 4ac
D = (1)2 - 4 x 2 x 4
D = 1 - 32
D = -31
Hence D < 0
∴ There is no real root.
∴ Solution cannot be made of 2x2 + 1x + 4 = 0